Jonathan wrote:

> I thought the convention was that \\(x \le y\\) means "given x we can get y".

I screwed up Lecture 18 but I've fixed it: now \\(x \le y\\) means "we can get \\(x\\) from \\(y\\)". If you get mixed up (as I often do), just remember 5 dollars \\( \le \\) 10 dollars: you can get less from more, not the other way.